# What are the steps to suggest a ARIMA model for a time series?

I'm having some troubles to "suggest" ARIMA models based only in the series plot, autocorrelation and partial autocorrelation function.

In the time series below, the first plot is the serie (no description of time), the second and third are Autocorreation and Partial Autocorrelation.

When the series have trend I know that is not stationary and need differencing, but in this case there is no trend. Apparently this series is nonstationary because the mean look bigger at start, but how can I simply by looking at the series identify that it has mean and constant variance?

This is some slides that I'm using Forecasting using R. There is some statement that say "The ACF of stationary data drops to zero relatively quickly", but how fast? In this case the ACF drops fast, but in some point the autocorrelatios become negative significant.

The plot of Partial Autocorrelation Function shows significant values at lag 1, 2 and 12.

I should consider a model with 1 difference?

What I think in general:

• The mean at first seems to me to be higher than in the other parts of the process, which indicates that the series is not stationary.

• The behavior of ACF and PACF looks like an Autoregressive Model

• With a time series like this the plot of the original series does not really suggest a change in mean. The series is suppose to have some random variation. The autocorrelation function and the partial acf give a better pictures. The acf shows an exponential decline indicative of a stationary autoregressive process. Taking that into account with the pacf only having the first lag significant and highly so I would choose AR(1). Keep in mind more than one model could fit well to your data. George Box would recommend parsimony meaning given a set of models to pick from choose the simplest. Dec 31, 2016 at 19:09
• Parsimony is a good principle as a guide for picking a model that is likely to be better at forecasting. @Irish Stat should be consulted on this. He has been doing this for a living for several decades beginning with his autobox product. Often he will ask for your data and then work the problem himself and then come back to the site with lts of graphs and a detailed answer. Dec 31, 2016 at 19:14
• @MichaelChernick ... nice words .. tu . OP please post your original data and I will try explain the sequence off steps to form a "useful model" . Dec 31, 2016 at 19:24
• I would say and maybe IrishStat would agree with me. You don't take seriously estimates that barely exceed the threshold for significance. Since you are looking at so many lags those two case that barely exceed the threshold should be ignored. Also no other pattern is there to suggest a better model. Dec 31, 2016 at 19:46
• @Roland If you are taking a time series course,you shouldn't be relying on us this much. You should be studying from your text and classroom notes and speaking with your professor when you are confused. I think CV should only be used to give you general hints about concepts. The self-help tag only tell us that you are interested in specific questions about a subject you are studying on your own. It is a little misleading to us to show us a series of very specific questions that are all part of a course you are taking. Dec 31, 2016 at 19:53